Question 1198979
To help Alec decide between the **45% ownership** and the **6.5% bond**, we analyze and illustrate both options under different scenarios for the success of the fast food chain.

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### **Option 1: 45% Ownership**
- Alec would own 45% of the fast food chain's profits (or losses).
- The future value of this option depends on the success of the business.
- Define success rates with corresponding projected annual profits for the business:
  - **High success**: Annual profit = ₱3,000,000.
  - **Moderate success**: Annual profit = ₱1,500,000.
  - **Low success**: Annual profit = ₱500,000.
  - **Failure**: Annual profit = ₱0.

Alec’s share in profits is:
\[
\text{Alec's profit} = 0.45 \times \text{Business Annual Profit}
\]

#### **Ownership Illustration**
| Success Level | Business Annual Profit (₱) | Alec's Share (₱) |
|---------------|-----------------------------|------------------|
| High          | 3,000,000                   | 1,350,000        |
| Moderate      | 1,500,000                   | 675,000          |
| Low           | 500,000                     | 225,000          |
| Failure       | 0                           | 0                |

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### **Option 2: 6.5% Bond**
- A bond offers a guaranteed annual return of **6.5%** on Alec’s ₱1,000,000 investment.
- Annual return:
\[
\text{Annual Bond Return} = 0.065 \times 1,000,000 = 65,000 \, \text{₱ per year}.
\]
This is a **fixed income** regardless of the success of the business.

#### **Bond Illustration**
| Success Level | Alec's Annual Return (₱) |
|---------------|---------------------------|
| High          | 65,000                   |
| Moderate      | 65,000                   |
| Low           | 65,000                   |
| Failure       | 65,000                   |

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### **Comparison of Both Options**
#### **1. Summary of Returns**
| Success Level | Ownership Share (₱) | Bond Return (₱) | Which is Better?         |
|---------------|-----------------------|-----------------|--------------------------|
| High          | 1,350,000            | 65,000          | Ownership significantly better |
| Moderate      | 675,000              | 65,000          | Ownership still better    |
| Low           | 225,000              | 65,000          | Bond better              |
| Failure       | 0                    | 65,000          | Bond significantly better|

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### **2. Risk and Reward Analysis**
- **Ownership (45%)**:
  - High risk: Alec's returns are dependent on the business's performance.
  - High reward: Substantial earnings if the business succeeds.

- **Bond (6.5%)**:
  - Low risk: Provides guaranteed returns regardless of business performance.
  - Lower reward: Fixed annual income of ₱65,000, which is small compared to potential high returns from ownership.

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### **Recommendation for Alec**
- If Alec is **risk-averse** and prefers stability, he should invest in the **6.5% bond** for consistent and guaranteed returns.
- If Alec is **risk-tolerant** and believes strongly in the business's success, the **45% ownership** is a better choice, as it offers potentially high returns in the long run.